In this article, we present the time-space Chebyshev pseudospectral method (TS-CPsM) to approximate a solution to the generalised Burgers-Fisher (gBF) equation. The Chebyshev-Gauss-Lobatto (CGL) points serve as the foundation for the recommended method, which makes use of collocations in both the time and space directions. Further, using a mapping, the non-homogeneous initial-boundary value problem is transformed into a homogeneous problem, and a system of algebraic equations is obtained. The numerical approach known as Newton-Raphson is implemented in order to get the desired results for the system. The proposed method's stability analysis has been performed. Different researchers' considerations on test problems have been explored to illustrate the robustness and practicality of the approach presented. The approximate solutions we found using the proposed method are highly accurate and significantly better than the existing results.

翻译：本文提出了一种时空Chebyshev伪谱方法（TS-CPsM）来逼近广义Burgers-Fisher（gBF）方程的解。该方法基于Chebyshev-Gauss-Lobatto（CGL）点，在时间和空间方向上进行配置。进一步地，通过映射，将非齐次初边值问题转化为齐次问题，并得到一个代数方程组。为了获得该方程组的期望结果，采用了Newton-Raphson数值方法。本文对所提方法进行了稳定性分析。通过探讨不同研究者考虑的测试问题，验证了所提方法的鲁棒性和实用性。使用该方法得到的近似解具有高精度，且显著优于现有结果。